What is the volume in cubic cm of a pyramid whose area of the base is 25 sq cm and height 9 cm?

### Concept & Volume of a Pyramid The volume of any pyramid is one-third of the product of its base area and its perpendicular height, regardless of the shape of the base (square, triangular, etc.). Volume Formula: $$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$$ ### Step-by-Step Solution 1. Extract the given values from the problem: Base Area ($A$) = 25 sq cm Height ($h$) = 9 cm 2. Apply the volume formula for a pyramid: $V = \frac{1}{3} \times A \times h$. 3. Substitute the given numbers into the formula: $V = \frac{1}{3} \times 25 \times 9$. 4. Simplify the expression by multiplying $\frac{1}{3}$ with 9 first: $V = 25 \times 3$. 5. Calculate the final result: $V = 75$ cubic cm. ### Exam Strategy & Shortcut You don't need to know what kind of polygon forms the base; the formula $V = \frac{Ah}{3}$ applies universally. Always look to divide the height by 3 first to make mental math trivial ($9/3 = 3$, $25 \times 3 = 75$). ### Common Pitfall A common mistake is treating the pyramid like a prism and forgetting to divide by 3 (which would incorrectly yield 225). ### Final Answer Therefore, the correct answer is **75**.